Strengthen bifurcation handler typing and align compartment/URL codec tests with actual guarantees

[Copilot]

This PR applies the requested review diffs across the MCP bifurcation handler and related tests. It removes unsafe typing/casts, improves fallback observability, and updates tests/docs to validate the intended behavior more explicitly and deterministically.

• Bifurcation handler: replace unsafe any with explicit types

  • Added a typed argument shape for handleBifurcationAnalysis inputs.
  • Replaced untyped dynamic import usage with a typed engine module contract plus runtime module-shape assertion.
  • Typed continuation/bifurcation result handling and removed rhsFn as any.

• Bifurcation handler: make fallback failures observable

  • Replaced empty catch with a logged warning that preserves fallback behavior while surfacing JIT compilation root cause.

• Compartment parity test: docs and parsing cleanup

  • Updated test docblock to match what is actually asserted (qualitative outcome + conservation, not quantitative rate-scaling verification).
  • Removed unnecessary nullish coalescing on execSync(..., { encoding: 'utf-8' }).
  • Corrected numeric parsing regex to reject invalid standalone decimal-point matches.

• URL state codec tests: stronger, clearer, deterministic assertions

  • Tightened malformed params warnings assertions to explicitly detect both malformed segments (kf:notanumber and empty ,, segment).
  • Added fallback coverage for empty/missing tab values.
  • Replaced compact/deflate magic numbers with named constants.
  • Replaced Math.random() in round-trip test data with deterministic values.

type BifurcationAnalysisArgs = {
  code?: string;
  max_steps?: number;
  parameter?: string;
  start_value?: number;
  end_value?: number;
};

const parsedArgs: BifurcationAnalysisArgs = (args ?? {}) as BifurcationAnalysisArgs;

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Original prompt

Please apply the following diffs and create a pull request.
Once the PR is ready, give it a title based on the messages of the fixes being applied.

[{"message":"The use of `as any` bypasses type safety. Define a proper interface for the expected argument structure to enable type checking and improve code maintainability.","fixFiles":[{"filePath":"packages/mcp-server/src/handlers/bifurcationAnalysis.ts","diff":"diff --git a/packages/mcp-server/src/handlers/bifurcationAnalysis.ts b/packages/mcp-server/src/handlers/bifurcationAnalysis.ts\n--- a/packages/mcp-server/src/handlers/bifurcationAnalysis.ts\n+++ b/packages/mcp-server/src/handlers/bifurcationAnalysis.ts\n@@ -2,8 +2,16 @@\n import { createToolResult, parseModelOrThrow, expandModel } from '../services/engine.js';\n import { structureError } from '../services/errors.js';\n \n+type BifurcationAnalysisArgs = {\n+  code?: string;\n+  max_steps?: number;\n+  parameter?: string;\n+  start_value?: number;\n+  end_value?: number;\n+};\n+\n export async function handleBifurcationAnalysis(args: ToolArgs): Promise<ToolResult<any>> {\n-  const parsedArgs = (args ?? {}) as any;\n+  const parsedArgs: BifurcationAnalysisArgs = (args ?? {}) as BifurcationAnalysisArgs;\n   try {\n     const engine = await import('@bngplayground/engine') as any;\n     const model = parseModelOrThrow(parsedArgs.code);\n"}]},{"message":"Dynamic import cast to `any` loses type information. Consider importing specific types from the engine package or creating a typed interface for the imported module.","fixFiles":[{"filePath":"packages/mcp-server/src/handlers/bifurcationAnalysis.ts","diff":"diff --git a/packages/mcp-server/src/handlers/bifurcationAnalysis.ts b/packages/mcp-server/src/handlers/bifurcationAnalysis.ts\n--- a/packages/mcp-server/src/handlers/bifurcationAnalysis.ts\n+++ b/packages/mcp-server/src/handlers/bifurcationAnalysis.ts\n@@ -2,10 +2,38 @@\n import { createToolResult, parseModelOrThrow, expandModel } from '../services/engine.js';\n import { structureError } from '../services/errors.js';\n \n+type EngineContinuationPoint = { stable: boolean };\n+type EngineBifurcation = {\n+  parameterValue: number;\n+  type: string;\n+  frequency?: number;\n+  criticalEigenvalues?: unknown[];\n+};\n+type EngineContinuationResult = {\n+  bifurcations: EngineBifurcation[];\n+  path: EngineContinuationPoint[];\n+};\n+type EngineModule = {\n+  JITCompiler: new (model: unknown) => {\n+    compile: () => {\n+      rhs: (y: Float64Array, dydt: Float64Array) => void;\n+    };\n+  };\n+  continuation: (args: {\n+    nSpecies: number;\n+    rhsFn: (y: Float64Array, p: number, dydt: Float64Array) => void;\n+    initialState: Float64Array;\n+    parameterStart: number;\n+    parameterEnd: number;\n+    stepSize: number;\n+    maxSteps: number;\n+  }) => Promise<EngineContinuationResult>;\n+};\n+\n export async function handleBifurcationAnalysis(args: ToolArgs): Promise<ToolResult<any>> {\n   const parsedArgs = (args ?? {}) as any;\n   try {\n-    const engine = await import('@bngplayground/engine') as any;\n+    const engine = (await import('@bngplayground/engine')) as EngineModule;\n     const model = parseModelOrThrow(parsedArgs.code);\n     const expandedModel = await expandModel(model);\n \n"}]},{"message":"Empty catch block swallows errors silently. Consider logging the error or at least adding a comment explaining why errors are intentionally ignored here.","fixFiles":[{"filePath":"packages/mcp-server/src/handlers/bifurcationAnalysis.ts","diff":"diff --git a/packages/mcp-server/src/handlers/bifurcationAnalysis.ts b/packages/mcp-server/src/handlers/bifurcationAnalysis.ts\n--- a/packages/mcp-server/src/handlers/bifurcationAnalysis.ts\n+++ b/packages/mcp-server/src/handlers/bifurcationAnalysis.ts\n@@ -45,7 +45,11 @@\n         compiled.updateParameters?.(params);\n         compiled.evaluate(0, y, dydt);\n       };\n-    } catch {\n+    } catch (jitError: any) {\n+      // Fallback is intentional, but log the root cause for observability/debugging.\n+      console.warn(\n+        `[bifurcationAnalysis] Failed to compile JIT RHS; falling back to zero RHS: ${jitError?.message ?? String(jitError)}`\n+      );\n       // Fallback: zero RHS (continuation will report no bifurcations)\n       rhsFn = (_y: Float64Array, _p: number, dydt: Float64Array) => {\n         for (let i = 0; i < nSpecies; i++) dydt[i] = 0;\n"}]},{"message":"The documentation claims the test verifies volume-based rate scaling with expected effective rate k/V = 0.5, but the test implementation (lines 155-166) does not validate this rate scaling. It only checks that C was produced and molecules are conserved. Either add assertions to verify the rate scaling or update the documentation to accurately reflect what the test validates.","fixFiles":[{"filePath":"tests/parity-compartment.spec.ts","diff":"diff --git a/tests/parity-compartment.spec.ts b/tests/parity-compartment.spec.ts\n--- a/tests/parity-compartment.spec.ts\n+++ b...